Category Archives: Combinatorics

A good title for this blog post exists, but I don’t know what it is

Today we will look at one of my favorite topics in combinatorics: the probabilistic method. Championed by Paul Erdős in the 1940’s, the probabilistic method has since become a staple in extremal and Hungarian-style combinatorics. While the applications of the probabilistic method … Continue reading

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What are Permutation Patterns?

Today we examine a topic known as combinatorial pattern avoidance. There has been an explosion of interest in this field of late; see, for instance, the international permutation patterns conference, or any recent issues of your favorite discrete mathematics journal. I was … Continue reading

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On the geometric mean of the binomial coefficients

Today we prove a remarkable asymptotic result regarding the binomial coefficients. Namely, let . We will show Before getting to the proof, I should say that this is most definitely not my creation; I believe the first publication of this … Continue reading

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